Metoda homogenizacije u topološkoj optimizaciji

master's thesis

• Author: Nela Ševerdija
• Mentor: Josip Tambača (mentor)
• Committee member: Josip Tambača (predsjednik povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Mladen Jurak (član povjerenstva)
• Committee member: Marko Tadić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2017-09-28, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu iznesen je kratki pregled primjene metode homogenizacije na problem topološke optimizacije dvodimenzionalne elastične strukture načinjene od izotropnog elastičnog materijala. Najprije je uveden pojam H-konvergencije na kojem je temeljena metoda homogenizacije. Izvedeni su uvjeti optimalnosti takve strukture, takozvane Hashin-Shtrikmanove ocjene, te je dokazano da se struktura maksimalne krutosti postiže sekvencijalnim laminatom ranga 2 za čije su određivanje izvedene eksplicitne formule. Konačno je implementiran algoritam kojim su izračunate optimalne strukture u odabranim primjerima.

Abstract (english)

In this thesis we present a short summary of the homogenization method and its application to problems of shape optimization in the elasticity setting in two dimensions when the domain is filled with an isotropic elastic medium. First we introduce the notion of H-convergence on which the method of homogenization is based. Next, the optimality conditions for such a structure, namely Hashin-Shtrikman energy bounds, are computed and it is proved that an optimal shape in terms of compliance could be achieved by a rank-2 sequential laminate for which the effective properties are then explicitly determined. Finally, a numerical algorithm is developed and applied to computing the optimal shape of a structure in a few select examples.

• Keywords: homogenizacija; topološka optimizacija; izotropni elastični materijal; Hashin-Shtrikmanova ocjena
• Keywords (english): homogenization; shape optimization; isotropic elastic medium; Hashin-Shtrikman energy bounds
• Language: croatian
• URN:NBN: urn:nbn:hr:217:789883
• Study programme: Title: Applied Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-03-15 14:15:05